A paddle boat can move at a speed of 20 ​km/h in still water. The boat is paddled 6 km downstream in a river in the same time it takes to go 3 km upstream. What is the speed of the​ river?

1 Answer
Nov 14, 2017

OK, let's try this...

Explanation:

In kinematics:
x_t = v_0 . t + x_0
x_0 (startpoint) is not important here, so:

x_t = v_0 . t;

x_"out" = 6 km;
x_"back" = 3 km;
t_"out"= t_"back";
v_"out"= v_"boat" + v_"river";
v_"back"= v_"boat" - v_"river";

rarr x_"out" = 2x_"back";
rarr v_"out".t = 2v_"back" . t;

Divide by t, as this is same for outgoing and return,
rarr v_"out" = 2v_"back" ;

v_"out" = v_"boat" + v_"river" ;
v_"back " = v_"boat" - v_"river" ;

rarr v_"boat" + v_"river" = 2(v_"boat" - v_"river")
rarr v_"boat" + v_"river" = 2v_"boat" - 2v_"river"
rarr v_"river" = v_"boat" - 2v_"river"
rarr 3v_"river" = v_"boat"
rarr v_"river" = v_"boat" /3

v_"boat" = 20 "km/hr", rarr v_"river"= 20/3 = 6 2/3 km/hr....